Stair shape maths GCSE coursework

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Introduction

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Coursework – Number Stairs

In order to investigate the stair shapes, I will look at the relationship among the total of 3 step stair shapes and position of stair shapes, on a 10 × 10 number grid. The shaded area, in the grid, is a 3 stair shape at position 25. The position is shown on the bottom left of every stairs. I will investigate different positions and their totals, on the 10 × 10 number grid, with the 3 stair shape (to begin with). With these results, I will be able to create a formula to show the total of 3 step stair shape, at any position, on a 10 × 10 number grid.

I will investigate further, by looking at the relationship between the different sized stair shapes, and the different sized number grids. 3 stair shape I will begin my investigation by obtaining enough results to formulate an a equation, for a 3 step stair shape I will began my investigation by obtaining enough results to formulate an equation, for a 3 step stair shape.

First I will draw a 3 stair shape at the bottom left with the number 1.

The Formula = 6n +40, how I get the 6n is mentioned above now I am going to show how I get the 40.

This shows the six n and numbers. 18+9+10+1+2= 40

This is how I get 6n +40 which will work on finding any 3 step stairs at least that’s what I think.

This is how I worked out my formula:

T = n + (n+1) n + 2 + n + 9 + n +10 + n + 18 = 6n+40

6n + 40 will work with any number in this 9 × 9 grid and with any 3 step stairshape.

The difference between a 10× 10 grid and a 9 × 9 is that to find a total of 3 step stair in a 10× 10 grid is that the formula is different 6n +44 from a 9 × 9 grid which is 6n + 40 this is the result of my investigation.

I am going to investigate the further relationship between the stair totals and other step stairs on an other number grid. For this I am going to use 8× 8 and a 3 step stair shape.

+ (-3g + 3) PART 3 I will now use grids and L-Shapes of different sizes; I will try more transformations and combinations of transformations. I will look into the relationship between the L-Sum, the L-Number, the grid size and the transformations.

Therefore, they cancel each other out to leave z. 8) Conclusion After this justification, it can now be said that for every 2x2 box on a Width z Grid, the difference of the two products will always be z. 9)

= n2+29n+nw Stage B: Bottom left number x Top right number = (n+30)(n+w-1) = n2+nw-n+30n+30w-30 = n2+nw+29n+30w-30 Stage B - Stage A: (n2+nw+29n+30w-30)-(n2+29n+nw) = 30w-30 When finding the general formula for any number (n), both answers begin with the equation n2+nw+29n, which signifies that they can be manipulated easily.

+ (4x15) T= 6+60 T=66 The total for all the stair values added together without a formula is= 1+2+3+16+17+31= 70 [The stair total for this 3-step stair is 70] My general formula to find the total values in a 3-step stair on a 15 by 15 grid is incorrect.